Answer:
She would have to do 219 haircuts in a month for the costs to be the same, which would be $428.
Step-by-step explanation:
To find this we take the costs of the first place.
$438
Next we can look at the costs of the second place using x as the number of haircuts she'd do.
2x
Now we can set the two equal to each other to find the number of cuts.
438 = 2x
219 = x
1. Decompose all numbers into prime factors
300 2 150 2 75 3 25 5 5 5 1 400 2 200 2 100 2 50 2 25 5 5 5 1 500 2 250 2 125 5 25 5 5 5 1
2. Write all numbers as the product of its prime factors
Prime factors of 300 = 22 . 3 . 52
Prime factors of 400 = 24 . 52
Prime factors of 500 = 22 . 53
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 2 , 5
Common prime factors with the greatest exponent: 24, 53
Uncommon prime factors: 3
Uncommon prime factors with the greatest exponent: 31
4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 24. 53. 31 = 6000
